Method of monitoring patient compliance with medications prescriptions

ABSTRACT

A method of monitoring compliance of a patient that has been placed on a medication maintenance program with a prescribed medication dosage by determining a normalized urine methadone concentration. An unadulterated urine sample is obtained from the patient. The urine methadone concentration and urine specific gravity are measured. The normalized urine medication concentration is calculated as a function of the measured medication concentration in the urine and the urine specific gravity. The calculated normalized urine medication concentration is compared with an expected medication concentration value for the patient for the maintenance program prescribed to determine any significant differences therebetween as an indication of noncompliance. 
     Alternatively, a urinary-parameter normalized urine medication concentration is calculated as a function of the measured medication concentration in the urine, the urine specific gravity and at least one selected pharmacokinetic parameter of the medication. The calculated urinary-parameter normalized urine medication concentration is compared with an expected medication concentration value for an average compliant patient for the maintenance program prescribed to determine any significant differences therebetween as an indication of noncompliance.

REFERENCE TO RELATED APPLICATION

This is a continuation-in-part of Application Ser. No. 08/145,821 filedNov. 2, 1993.

TECHNICAL FIELD

The present invention relates to therapeutic drug ingestion monitoring.More particularly, the invention relates to methods of monitoringpatients who are being prescribed potentially abusable or dangerousmedications and have been placed on medication maintenance programs forcompliance therewith.

BACKGROUND OF THE INVENTION

In the field of medicine and psychiatry, a number of medications, suchas opioids, sedative-hypnotics, anticonvulsants, neuroleptics, andantidepressants, have been found safe and efficacious for the treatmentof patients with biologically-based mental and physical illnesses.Patients placed on prescribed medication treatment plans are typicallymonitored. Subjective and objective methods are used to identifybothersome symptoms and to implement any changes necessary during thecourse of treatment. Monitoring generally continues for as long astreatment is provided. For example, the Hamilton Anxiety Scale can beused to quantify the amount of anxiety remaining as treatment proceeds.If the level of residual anxiety decreases significantly, say from theproper prescription of a benzodiazepine drug like diazepam, then thephysician and patient can be assured that treatment is efficacious andshould be continued.

Preferably both quantitative and analytical methods should be used tofollow the patient on a repetitive basis to insure that the patient isindeed ingesting the prescribed amounts of medication in the propermanner and responding as expected. Currently, the most common method ofmonitoring patients for medication compliance is clinical observationwhich involves individual counseling and close personal supervision byphysicians. Physicians observe physiological signs and symptoms such asintoxication, drug withdrawal typically occurring for benzodiazepines,barbiturates and opioids, or residual signs of illness such as tremor inanxiety, sighing in depression, and nociception in pain syndromes.Physicians also listen to patient complaints regarding degree of painrelief and evaluate psychological changes over time. This method howeveris time consuming, expensive and highly subjective. Needless to say, itis fraught with potential errors.

Additional compliance information can be obtained using qualitativeurine monitoring methods such as the standard laboratory procedurecalled enzyme-multiplied immunoassay (EMIT). Utilizing an arbitrarycutoff value, these methods provide the clinician with a simple positiveor negative indication of the possible presence or absence of a parentdrug or its metabolites in a patient's urine. The parent drug is theprescribed medication itself and the metabolites are those chemicalderivatives of the medication which naturally occur upon the patient'sbody metabolizing the medication. These tests do not provide informationconcerning the time or amount of last drug use or whether or not theprescribed dose of medication was ingested properly, diverted orsupplemented.

Physicians utilizing only clinical evaluation and qualitative urine drugscreening test results may develop problems in their treatment methods.Such is often the case in treating patients who have becomebiochemically dependent upon opioids either through prescription orillegal use. Opioid addicts experience great difficulty eliminatingtheir dependency upon such drugs and typically enter into extendedrehabilitative treatment programs which utilize prescribed methodonedosages to eliminate opioid dependency. Physicians must effectivelyassess the condition of patients on methadone maintenance programs inorder to adjust dosages and monitor compliance. If a patient iscontinually testing positive for opioids or complains of continuingsubjective opioid withdrawal symptoms, a physician may conclude that thecurrently prescribed dose of methadone is not sufficient to curb thebody's desire for opioids and may increase the prescribed dosage. Thishighly subjective monitoring method can result in over-medication,patients being given more methadone than they require, creating anunnecessary reliance on methadone. Alternately, physicians sometimesconclude, erroneously, that a patient's methadone dose should besufficient to prevent opioid withdrawal and drug cravings and deny thepatient a further increase sufficient to stop illicit opioid use. Suchaction can expose the patient to further intravenous drug use and theassociated negative social and medical consequences which can followsuch as HIV, hepatitis, and blood poisoning.

Similar problems with treatment may arise for patients prescribeddiazepam for longstanding generalized anxiety. Patients may not showimprovement in their condition even though this therapy is known to behighly efficient. This medication is a member of the sedative-hypnoticfamily of benzodiazepines which have been clinically shown to causesedation, hypnosis, decreased anxiety, muscle relaxation, anterogradeamnesia and anticonvulsant activity. A patient, for example, may insistthat he or she is ingesting the medication as prescribed, and yet claimno significant improvement in symptomology. The physician suspects thatthe patient is not ingesting the medication properly and perhaps isselling it, and orders a qualitative urine drug screen to verifycompliance. The screen is reported as positive at greater than 200 ng/mldrug concentration. Since some benzodiazepine is present the physicianassumes, incorrectly, that the patient is compliant, but will requireadditional medications and increases the daily dose. In truth, thepatient is diverting the majority of his or her dose to the illicitmarket and only ingesting enough drug to test positive on the drugscreen.

Patients also commonly visit multiple physicians to obtain similarmedication for self-ingestion. These patients desire the intoxicatingeffects of the medication, but are unable to obtain sufficientquantities from a single source. Qualitative tests like the EMIT aregenerally not useful in detecting this situation since the quantitativeamount of medication concentration in the body is not measured.

Another monitoring method sometimes used, though most often only inresearch centers, is direct measurement of parent drug concentrations oractive metabolites concentrations of the drug in plasma. This method hasbeen particularly useful to eliminate illicit opioid use of patients onmethadone maintenance programs. It is known from analytical studiesusing venous blood samples obtained from stable patients that plasmamethadone concentrations ranging from 150-600 ng/ml are necessary. Thisdirect method is not very practical since it requires the use of timeconsuming, expensive, and highly technical analytical procedures such ashigh pressure liquid chromatography and gas chromatography/massspectrometry since active and inactive metabolites must be quantifiedseparately. Additionally, for many patients the obtaining of plasmasamples is invasive, offensive and difficult due to inadequate venousaccess. Medical professionals must also be concerned about their ownhealth safety in doing this since they are exposed to blood productsfrom patient groups which can have a high prevalence of hepatitis andHIV infection. Therefore, such procedures are primarily conducted inresearch centers and not generally utilized in standard maintenanceprograms.

While providing useful information relative to patient status andtreatment compliance, the clinical monitoring methods described above,i.e. clinical interviews with patients, direct plasma drug measurementand qualitative urine drug screening, have distinct drawbacks whichlimit their usefulness in extended treatment programs. Therefore, it isseen that a need remains for a better method of monitoring patients whohave been placed on potentially abusable and dangerous maintenancemedications for compliance therewith. To help prevent continuedmedication misuse and better optimize patient medication dose, it wouldbe advantageous for patients to have a facile bodily fluid, such asurine, regularly and quantitatively monitored for the presence of themedication. Such a monitoring method would help physicians both inprescribing adequate doses of medication and in monitoring patients toinsure that they were only ingesting the prescribed amounts. Obtaining afluid sample like urine would not be invasive to the patient or a safetyrisk to the health care provider. Accordingly, it is to the provision ofsuch improved methods that the present invention is primarily directed.

SUMMARY OF THE INVENTION

In co-pending Application Ser. No. 08/145,821 it is disclosed thatpatients in methadone maintenance programs can be monitored forcompliance by sampling and analyzing a patient's urine for methadoneconcentration as an indicator of plasma methadone concentration which inturn provides a correlation to methadone dose ingested. This informationis used to monitor the patient's compliance with a prescribed methadoneprogram and to establish the proper methadone dose. First, it ispreferable to determine whether the urine sample is indeed from thepatient in question and whether the urine sample is adulterated as bycomparing urine pH, specific gravity, and creatinine level with that ofnormal urine and specific values previously determined for the patient.If found to be unadulterated and probably from the patient in question,the raw urine medication concentration is measured with standardquantitative laboratory methods. For example, the urine sample may bemeasured using high pressure liquid chromatography or gaschromatography/mass spectrophotometry, but preferably by usingfluorescence polarization immunoassay (FPIA) because of its ease andrapidity of analysis. FPIA is employed such as with an Abbott TDX or ADXAnalyzer.

Once an analytical value has been determined for the actualconcentration of methadone in the sample, adjustments are made toaccount for the effects of variations in certain urinary parameters uponthis concentration. A relationship exists between the actualconcentration of methadone adjusted for compounding effects of urinespecific gravity, the renal clearance of methadone as a function ofurine pH, and the concurrent plasma methadone concentration. Byobtaining multiple urine samples from a patient, once or twice a week,it is possible to establish a stable, baseline, 24-hour trough plasmamethadone concentration for each patient against which a current orfuture value can be statistically compared.

It was also disclosed that the actual urine methadone concentration canbe converted to a urinary parameter-normalized urine methadoneconcentration. The calculation incorporates the measured actual urinemethadone concentration, urine specific gravity, and the pharmacokineticparameters associated with metabolizing methadone of methadone dose,patient's body weight, and urine pH. By establishing an individual'sexpected value for the urinary-parameter normalized urine methadoneconcentration, subsequent readings may be compared with the expectedvalue to evaluate whether the patient is compliant with his or herprescribed dose.

It has now also been discovered that a patient's urine may also beanalyzed for parent drug and its metabolites concentrations as a methodof monitoring compliance with a prescribed medication dosage.(Hereinafter the term "medication concentration" and "parent drugconcentration" shall also be understood to include their metabolites.) Anormalized urine medication concentration (nu) is determined by arelationship discovered to exist between urine specific gravity and rawurine parent drug and its metabolites concentrations. Aurinary-parameter normalized urine medication concentration (nu_(p)) mayalso be determined by the pharmacokinetic manipulation of the normalizedurine medication concentration. Both nu and nu_(p) are utilized once orrepetitively for determining patient compliance with prescribedmedication dosage.

The normalized urine medication concentration is a constant value foreach patient and may be compared to an individual's expected nu oncesuch is established or to a group of nu. The individual's expected nu isestablished by obtaining multiple urine samples from a patient once ortwice a week and evaluating those samples for nu to obtain historicaldata on that patient. If the current nu is compared to and found to besimilar to the expected nu, then the patient is deemed in compliance.This method of monitoring compliance is dependant upon the assumptionthat a patient is initially compliant in order to obtain the expectedvalue.

In determining normalized urine medication concentration the urine ispreferably first tested for adulteration in the same manner as discussedabove. If found to be unadulterated, the urine methadone concentrationis measured with standard quantitative laboratory methods, preferablyFPIA. Once an analytical value has been determined for the rawconcentration of medication in the urine sample, a normalized urinemedication concentration is calculated in accordance with itsrelationship to specific gravity as hereinafter described.

Alternatively, for clinical situations the urinary-parameter normalizedurine medication concentration is preferably utilized since anindividual's expected value need not be established. Instead, theurinary-parameter normalized urine medication concentration is comparedwith an expected nu_(p) value of an average patient for the maintenanceprogram prescribed. This method is particularly applicable forpotentially abusable or dangerous medications such as antidepressants,anticonvulsants, beta-blockers, alpha agonists and antagonists,neuroleptics, analgesics, antirheumatics, and chemotherapy agents.

The nu_(p) is calculated by adjusting the normalized urine medicationconcentration for compounding effects of urine pH, medication dose,patient body weight, urine flow rate and other pharmacokineticparameters associated with the metabolism of a particular drug. Theexpected nu_(p) value of an average patient was established by obtainingnumerous samples of controlled compliant patients on prescribed doses ofmedication and evaluating those samples for nu_(p). If the current valueof the nu_(p) is within ±20 percent of the nu_(p) value expected of theaverage patient on the same prescribed dose, the patient is consideredto be in compliance with his or her prescribed dose.

Compliance may also be confirmed by using the current urinary-parameternormalized urine medication concentration to estimate the correlatingdaily medication dose from a previously developed empirical graph ofurinary-parameter normalized urine medication concentration (ng/ml)versus daily oral medication dose ingestion (mg/day) for the generalpopulation. If the estimated daily medication dose is not the prescribedmedication dose, then the patient is not in compliance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a preferred method of the invention as itrelates to a methadone maintenance program.

FIG. 2 is a block diagram of another preferred method of the inventionas it relates to a methadone maintenance program.

FIG. 3 is a graph of measured methadone renal clearance versus urine pH.

FIG. 4 is a graph of reverse urine creatinine excretion factor (RUCEF)versus urine volume production rate factor (UVPRF).

FIG. 5 is a graph of urine volume production rate factor (UVPRF) versusspecific gravity factor (SGF).

FIG. 6 is a graph of plasma methadone concentration versus daily oralmethadone dose.

FIG. 7 is a graph of plasma methadone concentration calculated using themethod of the present invention versus measured plasma methadoneconcentration using Abbott fluorescence polarization immunoassay (FPIA).

FIG. 8 is a graph of urine methadone concentrations simultaneouslymeasured by FPIA and gas chromatography/mass spectrometry (GC/MS).

FIG. 9 is a block diagram of a preferred method of the present inventionas it relates generally to monitoring medication maintenance programs.

FIG. 10 is a graph of urinary-parameter normalized urine diazepamconcentration versus daily oral valium dose ingested.

FIG. 11 is a graph of urinary-parameter normalized urine alprazolamconcentration versus daily oral xanax dose ingested.

FIG. 12 is a graph of urinary-parameter normalized urine alprazolamconcentration versus daily oral xanax dose ingested showing patientstandard deviations and mean levels.

FIG. 13 is a graph of urinary-parameter normalized urine opiateconcentration for codeine versus daily oral medication dose ingested.

METHADONE MAINTENANCE PROGRAMS

For methadone maintenance programs, the optimum 24-hour trough plasmamethadone concentrations is between 150-600 ng/ml, which has beengenerally recognized in past studies as most effective in deterringillicit opioid use. A patient's 24-hour trough plasma methadoneconcentration, as calculated by the present method, is compared to apreviously developed empirical graph of plasma methadone concentration(ng/ml) versus daily oral methadone dose ingestion (mg/day) for thegeneral population. The graph, as shown in FIG. 6, represents the24-hour trough plasma methadone concentration expected for the averagepatient comprising the cohort from which the general population data wasgenerated. The comparision helps a physician determine both how thepatient is metabolizing methadone, what the most likely final methadonedose will be to attain the 150-600 ng/ml level, or whether the patientis compliant with his or her prescription.

Over time, a unique plasma concentration-daily methadone doserelationship is derived for each individual patient which can becompared to the relationship expected for that particular patient or foran average patient. If the two relationships are not similar, thepatient's metabolism rate may account for any over- orunder-effectiveness of the prescribed dose. A physician, in accountingfor the patient's individual metabolism rate, can now optimize thepatient's methadone dose to achieve an efficacious and safe plasmamethadone concentration. Further, once the optimum methadone dose isestablished for the patient, the physician can monitor the patient forcompliance with his or her prescribed dose by comparing the plasmamethadone concentration of methadone, as calculated by the presentmethod, with his expected, historical plasma methadone concentration forthat particular methadone dose to reveal any covert methadone diversionor supplementing.

Testing for Adulteration

First, a supervised, spot sample of urine is collected from a patient.Several properties of the urine are measured to evaluate whether theurine is adulterated, adulteration being the altering by a patient ofhis or her urine in an effort to prevent detection of illicit drug useor diversion of methadone. Adulteration typically is accomplished byadding foreign substances to the urine such as salt, bleach, or vinegar.Many patients attempt to dilute amount of drugs in the urine sample bydrinking large quantities of water or by adding water to the sample.Adulteration may also occur by substituting another person's urine forthe patient's own urine, including instillation of foreign urine intothe patient's bladder.

In checking for adulteration, urine pH is measured, as with the use of apH Data Logger type meter available from Oakton, to see if it is withinthe normally expected pH range of 4.5 to 8.5. Urine specific gravity isalso measured to see if it is within the normal range of 1.004 to 1.035units. A Digital Urinometer by Biovation may be used for this test.Creatinine, an end product of glycine and arginine metabolism excretedthrough the kidneys, is measured to evaluate renal function. Thecreatinine level in human urine usually ranges from 8 to 500 mg/dl, therange being affected by variables such as age, sex, diet, lifestyle andgeographic location. Creatinine levels generally are homeostaticallymaintained by the body at a constant value for each individual patientover his or her lifetime. Creatinine levels may be determined on manydifferent analyzers, including a TDx REA Creatinine System availablefrom Abbott Laboratories. All of these tests are helpful in establishingnormally expected ranges for each patient and the overall population ofpatients.

Once pH, specific gravity, and creatinine level values for the spoturine sample are obtained for a particular patient, comparisons can bemade between the sample in question and values previously measured (ifalready available) both for the patient and for normals to ascertainwhether the urine sample is adulterated. If no adulteration is found, adata base is created or extended for the patient so that a basis ofcomparison exists for future spot urine samples. Of the three measures,urinary creatinine level is generally the most useful indicator as towhether the spot sample is that of the patient or of someone else.

Determination of Raw Urine Methadone Concentration

The unadulterated sample is next analyzed for raw urine methadoneconcentration, preferably using fluorescence polarization immunoassay(FPIA) technology. In this regard an Abbott TDX or ADX Analyzer may beprofitably employed. Other standard analytical methods may also be usedsuch as chromatography or other types of immunoassay. The value obtainedis the raw urine methadone concentration, u.

Determination of Plasma Methadone Concentration

Plasma methadone concentration is obtained from the raw urine methadoneconcentration by utilizing a standard dimensionally correct relationshipknown as the renal clearance, which is,

    cl==(u·v)/p                                       (1)

where cl is renal clearance (ml/min), u is raw urine methadoneconcentration (ng/ml), v is the volume of urine collected in time(ml/min) or otherwise known as the urine volume production rate, and pis the measured plasma methadone concentration at the midpoint of thecollection period (ng/ml).

Since the actual, current renal methadone clearance is not generallyknown for any one patient, nor can it easily be directly measured undernormal clinic conditions, it must be estimated from an empiricalrelationship. From experiments measuring urine and plasma methadoneconcentrations over timed collection periods (which recognizes that therenal clearance for methadone is strongly affected by urinary pH becauseof the weakly basic properties of methadone), it has now been found thatrenal clearance relates to urine pH in the range 4.8-8.7 (see FIG. 3)as,

    cl=104,218·pH.sup.(-4.76)                         (2)

and for which generally, a strong dependence upon actual patient weightis not noticed.

Rearranging Equation (2), the plasma concentration of urine may becalculated as follows,

    p=u·v/cl                                          (3)

The actual, raw urine methadone concentration is known from the FPIAresults. Renal clearance can be calculated from Equation (2) byutilizing the urine pH previously measured in testing for adulteration.However, actual values of the urine volume production rate, v, are notavailable since routine clinical urine sampling procedures only providea point-in-time or spot urine sample.

Heretofore, it has been thought to be impossible to calculate plasmamethadone concentration of a drug from the spot urine sample and that atimed urine collection must be done (usually 24 hours). It has now beenfound that these beliefs are flawed.

It is now appreciated that renal excretion rates (mg/min) for drugs andurine metabolites are relatively constant for any patient during atypical day. This constancy has now been experimentally verified byexamining the renal excretion rates of methadone, benzodiazepines, otherdrugs and creatinine and other endogenous metabolites as a function ofurine volume production rate. For example, sequential, complete andtimed (1-8 hours holding periods) aliquots of urine for 12 compliantcontrol subjects were collected over 24 to 72 hour periods. For each andevery urine aliquot, urine volume production rate (ml/min), specificgravity and creatinine concentration (ng/ml) were determined.

Using this data, a dimensionless, linear relationship was found to existthat is the same for all patients, between a urine volume productionrate factor (UVPRF) and a reverse urine creatinine excretion factor(RUCEF). For each individual, control, urine collection period, theUVPRF is defined by the ratio of urine volume production rate for eachurine aliquot collected, v, to the urine volume production rate for themost concentrated sample in the collection period with a specificgravity usually near 1.030, v',

    UVPRF=v/v'.                                                (4)

The RUCEF factor is defined by the ratio of the creatinine concentrationof the most concentrated urine aliquot with a specific gravity usuallynear 1.030, u', to the creatinine concentration for each urine aliquotcollected, u,

    RUCEF=u'/u.                                                (5)

This linear relationship is shown in FIG. 4. The best fit linearregression line is given by the expression,

    RUCEF=0.942(SE 0.013)·UVPRF+0.121(SE 0.043)       (6)

    u'/u=0.942·v/v'+0.121                             (7)

adjusted squared multiple R=0.985, standard error (SE) ofestimate=0.242, F-ratio 4965.

Therefore, contrary to the traditional teachings of those skilled in theart, urine drug and metabolite concentrations, u, are inversely relatedto the volume of urine produced by the kidneys, v, clearly demonstratingthat the product (u·v) is constant at any particular time point andurine pH (given a steady-state plasma methadone concentration p andrenal clearance cl).

Since p, cl, and (u·v) at any time point and urine pH are constant,steady-state values, it follows that from Equation (7) some empiricalmathematical relationship must exist between u and v such that given anarbitrary urine volume production rate v' and an equivalent u' at areference point (specific gravity 1.030):

    {u·v}.sub.sg actual ={u'·v'}.sub.sg 1.030(8)

or upon rearrangement for u' gives,

    u'=u·(v/v')                                       (9)

where the products given in Equation (9) are those measured for a spoturine collected with an actual specific gravity and a corrected specificgravity typical of a morning void of 1.030.

Using controlled urine collections, a urine volume production rate v' of0.44 ml/min for persons with reasonably normal renal functions at aspecific gravity of 1.030 was measured. It has also been discovered thata linear relationship exists between the urine volume production ratefactor and the specific gravity factor (SGF),{(1.030--1.000)/(sg--1.000)}, as shown in FIG. 5 and given as follows:

    UVPRF=v/v'=2.43(SE 0.106)·SGF-1.43(SE 0.216)      (10)

where the adjusted squared multiple R=0.856, standard error of theestimate=0.787, F-ratio 482.

Combining all of the above considerations, plasma methadoneconcentrations can be calculated by substituting Equations (2, 8, 9 and10) in Equation (3): ##EQU1## where values of u, specific gravity, andpH are known from previous test results on a patient's spot urinesample. The equation may be more generally expressed as follows:

    p=k.sub.3 ·u·(k.sub.1 ·SGF-k.sub.2)/k.sub.4 ·pH.sub.(-k5)                                    (11a)

wherein k₃ is a constant approximately equal to 0.44, k₁ is a constantequal to 2.43, k₂ is a constant equal to 1.43, k₄ is a constant equal to104,218 and k₅ is a constant equal to 4.76.

Comparing Patient's Calculated Plasma Methadone Concentration to that ofan Average Patient for the Same Dose

Once the plasma methadone concentration is calculated from Equation(11), it is compared with the plasma methadone concentration expectedfrom an average patient on a similar daily methadone dose as shown inFIG. 6, which demonstrates how plasma methadone concentration varieswith dose for the standard population. FIG. 6 was developed by utilizingdata from 8300 urine samples from 150 methadone maintenance patients oncontrolled daily methadone dosages.

Using this figure, a clinician can estimate how a prescribed dose willeffect a patient's methadone plasma level. For example, a patient on a70 mg/day methadone dose is expected from FIG. 6 to have a plasmamethadone concentration of 200 ng/ml. However, from the spot urinesample the calculated plasma methadone concentration is 100 ng/mlthereby indicating that the patient's body is quickly metabolizing themethadone and a higher dose is needed or that the patient is divertingthe methadone to others or that the patient is simply not using it.Higher concentrations per dose suggest the opposite of the above.Knowing that the plasma methadone concentration does not correlate tothe prescribed methadone dosage, the clinician now has valuableinformation to evaluate the next step in the patient's program.

An optional use of the calculated plasma methadone concentration is forestimates of the methadone doses that a patient has taken. FIG. 6 isused to estimate the patient's methadone dose by adjusting thecalculated plasma methadone concentration relative to any parameters ofthe patient that fall outside the average patient parameters, such aspatient body weight, methadone plasma half-life, and time of ingestingdose.

Verification of Plasma Methadone Concentration Equation (11)

In order to ascertain the effectiveness of the plasma methadoneconcentration formulation, blood and urine samples were taken from acontrol group of patients. Urine and blood samples were simultaneouslyanalyzed for plasma methadone concentration using FPIA and GC/MS. Theurine methadone concentration was converted to a calculated plasmamethadone concentration utilizing the formulation of the presentinvention in Equation (11).

Referring now to FIG. 7, the accuracy of calculating plasma methadoneconcentration from urine methadone concentration is verified by theexcellent linear agreement between the plasma concentrations calculatedby the present method from random, spot urine measurements andconcurrently measured plasma methadone concentrations using actual bloodsamples: Estimated=0.970(SE 0.034)-Measured -1.25(SE 11.495), adjustedsquared multiple R=0.987, standard error of estimate=20.155, F-ratio810.

Determination of Urinary-Parameter Normalized Urine MethadoneConcentration

The parameters of a patient's urine, such as pH and specific gravity,vary from one day to the next dependant upon the type and quantities offoods and beverages ingested. Additionally, individuals metabolizesthese substances, as well as methadone, at different rates. To accountfor these variations, a urinary-parameter normalized urine methadoneconcentration, nu_(p), is calculated that adjusts measured raw urinemethadone concentration, u, in accordance with a prescribed methadonedose, urine specific gravity, patient's current body weight (lbs) andurine pH. The relationship between u, pH, dose and specific gravity wasempirically developed using nonlinear regression analysis. Results werenormalized to a dose level of 80 mg/day, a patient weight of 154 pounds,and urine pH of 6.5 giving the final equation for monitoring a patient'snu_(p) in Equation (12) as follows:

    nu.sub.p =(80/DOSE).sup.0.823 ·(6.5/pH).sup.-4.838 ·(BODY WEIGHT/154)·UVPRF·u

The equation may be generally expressed in Equation (12a) as follows:

    nu.sub.p =(k.sub.3 /DOSE).sup.k4 ·(k.sub.5 /pH).sup.-k6 ·(BODY WEIGHT/k.sub.7)·u·(k.sub.1 ·SGF-k.sub.2)

wherein k₃ is a constant equal to 80, k₄ is a constant equal to 0.823,k₅ is a constant equal to 6.5, k₆ is a constant equal to 4.838, k₇ is aconstant equal to 154, k₁ is a constant equal to 2.43 and k₂ is aconstant equal to 1.43.

The urinary-parameter normalized urine methadone concentration isstatistically constant and unique for each patient regardless of anindividual's methadone metabolism and daily changes in urine parameters.Thus, a patient's expected nu_(p), once established accurately for anindividual patient within a statistical margin of error, may be used toevaluate methadone diversion or supplementation in patients by comparingsubsequent calculations of nu_(p) with the patient's particular expectedvalue of nu_(p). If the subsequent calculation is similar to theexpected value, the patient is complying with his prescribed dose.

The generation of a patient's nu_(p) expected value is done usingstandard statistical techniques developed for relating the mean andstandard deviation observed from a particular sampling distribution (ofsize n elements) to the mean and standard deviation expected for thewhole population of values, both for each patient and the population ofall patients. For further details one can refer to the text, Hahn GJ,Meeker WQ, Statistical Intervals, John Wiley and Sons, 1991.

To utilize such techniques it is first necessary to determine what theexpected standard deviation is for the whole population of compliantpatients under observation. Previously, it had been observed thatalthough mean values for nu. are different for each patient, theobserved variability about the mean for compliant patients is quiteconsistent and similar to the overall cohort of compliant patients;suggesting that the following statistical technique can be utilized.

Sequential, urine data was retrieved from computer files for 216patients (13,000 data points) and transferred into a commercialstatistical/graphical package produced by Systat, Inc. Each patient'sdata was sorted individually by ascending concentration for initial datareview. All data points having unusual creatinine values <10 or >500mg/dl or a methadone concentration <300 or >60,000 ng/ml were discardedas being suspect and non-physiologic. Additional outliers wereeliminated from each patient file using manual review (preliminarystatistic data were available as a guide). For statistical reasons, allpatients having less than 10 acceptable data points were alsoeliminated.

Using the remaining data sets for each patient (180 persons,approximately 12,000 individual urine values), individual nu_(p) valueswere obtained from which individual means and standard deviations werecalculated.

Utilizing this data, a plot of sample size (for each patient) versuscalculated sample standard deviation (for each patient) was generated.Approximately, 180 individual, standard deviations (y-axis) were plottedagainst samples sizes ranging from 10 to 200 (x-axis). Using standard95% confidence limit

tables from Hahn and Meeker, lower and upper limits were co-plotted onthe above curve by adjusting the overall population standard deviationuntil the data bounded by the prediction curves enclosed all acceptabledata. The average population standard deviation for the set ofacceptably, compliant patients was found to be about 3000 for thisparticular set of patients, though it could be lower if furtherrestrictions to the initial data set were applied. In general, theaverage population standard deviation varies linearly with mean nu_(p),and considering this effect the acceptable range for a particularpatient can be narrowed.

Given this value, another set of prediction equations specifying theallowable range for the next measured nup for a particular patient,given a sample size of n, a mean nu_(p) for an individual patient andeither the patient standard deviation or the population standarddeviation (whichever is least), can be calculated as shown in Hahn andMeeker. If the measured value is within the acceptable statisticalrange, given a previously calculated mean and standard deviation, thenit is accepted. If the value is too high or too low, this is marked onthe urine drug screen under the column called Pred, as shown in clinicalcases #'s 4 and 5, Tables F and G.

An alternative method which can be used to establish outliers for eachpatient data set, which is also statistically sound, is based upon theratio of the currently determined nu_(p) to the mean nu_(p) calculatedfrom previous values for an individual (usually a minimum of 3 to amaximum of 12, though any larger mumber of samples could be used.) Byplotting log normal histograms of these calculated ratios for the samepatient data set mentioned above, the expected variation about the mostcommon value of unity for the entire population is determined.Ninety-nine percent confidence limits are distributed in a skewed mannerabout the value unity and range between about 0.43 to 2.30. Therefore,given a current mean nu_(p) for a particular patient, the acceptablevalues can be found by simple multiplication using 0.43 times nu_(p) forthe lower limit and 2.30 times nu_(p) for the upper limits. Otherconfidence intervals are easily determined as well.

Verification of Urinary-Parameter Normalized Urine MethadoneConcentration Equation (12)

Shown in Table A is a partial representation of data from a standardcomputer printout for a compliant patient in which is summarized bothurine parameters and methadone concentrations. The last column in thefigure represents the urinary-parameter normalized urine methadoneconcentration values for the patient which are quite constant once sg,pH, dose corrections are made to the raw urine methadone concentration.CR represents the specific gravity corrected urine creatinineconcentration which should have a CV of less than 15 percent.

                  TABLE A                                                         ______________________________________                                        Date  Dose   Temp    pH   SG    CR   u    p    nu.sub.p                       ______________________________________                                        04-20-                                                                              70     98.0    5.40 1.022 335  6838 167  6966                           92M                                                                           04-15-                                                                              70     96.0    5.70 1.024 268  6536 176  7381                           92W                                                                           04-13-                                                                              70     96.0    5.90 1.019 271  5462 259  10913                          92M                                                                           04-10-                                                                              70     98.0    5.70 1.021 377H 5180 177  7430                           92F                                                                           04-06-                                                                              70     98.0    5.90 1.028 261  7398 171  7208                           92M                                                                           04-02-                                                                              70     96.0    5.70 1.026 271  5990 149  6254                           92h                                                                           03-30-                                                                              70     94.0    5.60 1.021 303  4203 132  5532                           92M                                                                           03-25-                                                                              70     98.0    5.20 1.021 271  8469 187  7790                           92W                                                                           03-24-                                                                              70     98.0    6.00 1.023 243  3736 139  5852                           92T                                                                           03-20-                                                                              70     96.0    5.80 1.024 272  5601 164  6881                           92F                                                                           03-16-                                                                              60     94.0    5.30 1.022 286  7049 157  7448                           92M                                                                           03-13-                                                                              60     96.0    5.70 1.019 277  4935 199  9473                           92F                                                                                         Mean: 287    5950   173  7427                                                 SD:    35    1372   33   1492                                                 CV:    12.2   23     19.1                                                                               20                                                  Tests:                                                                               12     12    12    12                                    ______________________________________                                    

Clinical Examples

Case #1:

J. S. is a 52 year old woman with right-sided, migraine headaches withaura beginning after her hysterectomy at age and prior to regular use ofany medication. Her migraines began with flashes of light and blurryvision in either eye. Often "a film covers my right eye." Prodromata wasusually followed by right retro-orbital pain accompanied by photophobiaand nausea. This patient also suffered tension headaches and headachessecondary to allergic rhinitis. She was able to clinically differentiatemigraine and tension components of her headaches, as the migrainecomponent was refractory to multiple trials of ergot alkaloids,benzodiazepines, NSAIDs, beta-blockers, calcium channel blockers andpsychotherapy. Multiple CT scans had been normal. J. S. had beenbiochemically dependent upon prescription opioids to relieve migrainepain for over a year prior to her referral to a methadone maintenanceclinic. According to Federal Register 21 CFR Part 291, a personbiochemically dependent (this is the current definition for opioiddependency utilized by the federal government) to narcotics for morethan a year qualifies to enter into a methadone maintenance program.

J. S.'s situation was similar to that of approximately 0.5% of thegeneral, adult population of the United States who are alsobiochemically dependent upon opioid medications because of legitimatemedical illness and disease. Oftentimes, it is difficult for theclinician to determine whether or not the patient is currently usingopioids for relief from organic pain or is treating the psychologicalsequelae of their disability. In either case, methadone maintenance wasthe most efficacious choice to help and protect the patient.

J. S. enrolled in the methadone maintenance program 36 months ago forpain management. Gradual titration to 45 mg of methadone was achievedover a short time period during which migraines slowly decayed infrequency and severity. During her time in treatment she hadsubsequently suffered only 2 migraine attacks which were greatly reducedin intensity. Both attacks were related to a transient decrease inplasma methadone levels below 80 ng/ml secondary to vomiting associatedwith viral syndromes.

A urine history is shown in Table B for this patient showing bothestimated plasma methadone levels and the urinary parameter-normalizedmethadone concentration.

                                      TABLE B                                     __________________________________________________________________________    Date  Dose                                                                              Temp                                                                              pH  SG  CR  u   p  nu.sub.p                                     __________________________________________________________________________    07-01-                                                                              45  94.0                                                                              7.70                                                                              1.012                                                                             319 1069                                                                              348                                                                              21153                                        93h                                                                           06-21-                                                                              45  94.0                                                                              6.90                                                                              1.008                                                                             265 1336                                                                              401                                                                              25720                                        93M                                                                           06-14-                                                                              45  94.0                                                                              6.60                                                                              1.011                                                                             273 2109                                                                              368                                                                              22145                                        93M                                                                           06-07-                                                                              45  95.0                                                                              7.30                                                                              1.011                                                                             270 1883                                                                              399                                                                              32208                                        93M                                                                           06-03-                                                                              45  98.0                                                                              7.00                                                                              1.010                                                                             254  646                                                                              168                                                                              10174                                        93h                                                                           05-27-                                                                              45  94.0                                                                              7.60                                                                              1.018                                                                             269 1246                                                                              215                                                                              13051                                        93h                                                                           05-20-                                                                              45  95.0                                                                              6.80                                                                              1.011                                                                             275 1285                                                                              259                                                                              15585                                        93h                                                                           05-13-                                                                              45  95.0                                                                              7.80                                                                              1.011                                                                             272  757                                                                              293                                                                              17845                                        93h                                                                           05-03-                                                                              45  97.0                                                                              5.50                                                                              1.020                                                                             357H                                                                              4094                                                                              153                                                                               7585                                        93M                                                                           04-29-                                                                              45  94.0                                                                              6.70                                                                              1.014                                                                             N/T 1318                                                                              180                                                                              10815                                        93h                                                                           04-22-                                                                              45  96.0                                                                              6.80                                                                              1.020                                                                             320 3900                                                                              335                                                                              20168                                        93h                                                                           04-12-                                                                              45  94.0                                                                              7.20                                                                              1.009                                                                             260  915                                                                              310                                                                              18777                                        93M                                                                                         Mean:                                                                             285                                                                              1713                                                                             285                                                                              17265                                                            SD:  32                                                                              1146                                                                             90 5439                                                             CV:  11.3                                                                            66.8                                                                             31.2                                                                             31.5                                                             Tests:                                                                             11                                                                              12 12 12                                                 __________________________________________________________________________

Case #2:

A. N. is a 44 year old woman whose migraine with aura beganapproximately 20 years ago. Beginning with blurred vision, subsequentunilateral headaches were invariably accompanied by nausea and vomiting,photophobia, and hypersensitivity to motion of her head and to cigarettesmoke. Despite trials of biofeedback, physical therapy, and medications(trials of beta blockers, calcium channel blockers, ergot alkaloids overthe years) and drug holidays; the frequency of her headaches hadincreased over the years to nearly daily occurrence. Lumbar puncturesand multiple CT and MRI scans of her head were normal.

Following failure of self-administered IM administration of nalbuphineto control her pain, she began methadone maintenance 24 months ago.Because of many years of prior use of barbiturate-containing compoundsher hepatic metabolic function was significantly enhanced requiring morethan normal amounts of methadone-as shown by urine plasma concentrationestimates. After stabilization on 130 mg per day of methadone, hermigraines ceased completely at a plasma methadone level above 135 ng/ml.She continued to experience infrequent stress-related headaches, whichwere slowly decreasing in severity and frequency.

Urine histories are shown for this patient in Tables C and D. Notice howplasma methadone levels had increased in this patient over time ashepatic function returned to normal by discontinuingbarbiturate-containing compounds (bar).

                                      TABLE C                                     __________________________________________________________________________    Date  Dose                                                                             Temp                                                                              pH SG  CR bar                                                                              u  p  nu.sub.p                                      __________________________________________________________________________    06-01-91S                                                                           100                                                                              N/T 5.10                                                                             1.021                                                                             200                                                                              HI 6338                                                                             127                                                                              3243                                          05-29-91W                                                                           100                                                                              N/T 5.40                                                                             1.021                                                                             184                                                                              2370                                                                             1985                                                                             52 1339                                          05-25-91S                                                                           100                                                                              N/T 5.40                                                                             1.020                                                                             N/T                                                                              N/T                                                                              1360                                                                             39 995                                           05-22-91W                                                                           100                                                                              N/T 5.10                                                                             1.013                                                                             N/T                                                                              N/T                                                                              1511                                                                             62 1582                                          05-20-91M                                                                           100                                                                              N/T 5.10                                                                             1.005                                                                             134                                                                              HI  615                                                                             80 2026                                          05-18-91S                                                                           100                                                                              N/T 5.40                                                                             1.017                                                                             N/T                                                                              N/T                                                                              2067                                                                             76 1952                                          05-15-91W                                                                            80                                                                              N/T 5.40                                                                             1.019                                                                             129                                                                              HI 1120                                                                             35 1070                                          05-13-91M                                                                            65                                                                              N/T 5.70                                                                             1.009                                                                              72                                                                              HI  335                                                                             37 1367                                          05-11-91S                                                                            65                                                                              N/T 5.10                                                                             1.016                                                                             182                                                                              HI  816                                                                             25  911                                          05-08-91W                                                                            50                                                                              N/T 5.40                                                                             1.010                                                                             N/T                                                                              N/T                                                                               853                                                                             65 2924                                          05-06-91M                                                                            40                                                                              N/T 5.40                                                                             1.019                                                                             N/T                                                                              N/T                                                                               174                                                                             5  LOW                                           05-03-91F                                                                            40                                                                              N/T 5.40                                                                             1.009                                                                              89                                                                              HI  296                                                                             26 1389                                                          Mean:                                                                             141   1456                                                                             52 1709                                                          SD:  49   1661                                                                             32  769                                                          CV: 35.0   114                                                                             62.3                                                                              45                                                           Tests:                                                                             12    12                                                                              12  12                                           __________________________________________________________________________

                                      TABLE D                                     __________________________________________________________________________    Date  Dose                                                                             Temp                                                                              pH SG  CR bar                                                                              u  p  nu.sub.p                                      __________________________________________________________________________    04-04-92S                                                                           130                                                                              95.0                                                                              5.80                                                                             1.013                                                                             196                                                                              0  4915                                                                             373                                                                              7728                                          03-28-92S                                                                           130                                                                              98.0                                                                              5.90                                                                             1.020                                                                             210                                                                              0  6565                                                                             287                                                                              5944                                          03-21-92S                                                                           110                                                                              95.0                                                                              5.50                                                                             1.021                                                                             216                                                                              0  9651                                                                             278                                                                              6580                                          03-14-92S                                                                           110                                                                              97.0                                                                              5.70                                                                             1.022                                                                             210                                                                              0  8964                                                                             282                                                                              6703                                          03-07-92S                                                                           110                                                                              96.0                                                                              6.30                                                                             1.014                                                                             186                                                                              0  4471                                                                             395                                                                              10880                                         03-02-92M                                                                           110                                                                              95.0                                                                              5.60                                                                             1.022                                                                             206                                                                              0  8778                                                                             254                                                                              6025                                          02-21-92F                                                                           120                                                                              96.0                                                                              6.20                                                                             1.016                                                                             181                                                                              0  5169                                                                             403                                                                              8970                                          02-15-92S                                                                           120                                                                              98.0                                                                              5.90                                                                             1.015                                                                             187                                                                              0  4525                                                                             306                                                                              6778                                          02-08-92S                                                                           120                                                                              96.0                                                                              6.10                                                                             1.017                                                                             181                                                                              0  5506                                                                             364                                                                              8074                                          01-31-92F                                                                           120                                                                              95.0                                                                              6.20                                                                             1.016                                                                             218                                                                              0  6896                                                                             425                                                                              11966                                         01-18-92S                                                                           120                                                                              96.0                                                                              5.50                                                                             1.021                                                                             224                                                                              0  9503                                                                             274                                                                              6031                                          01-11-92S                                                                           130                                                                              96.0                                                                              5.30                                                                             1.020                                                                             182                                                                              0  9494                                                                             249                                                                              5117                                                          Mean:                                                                             200                                                                              0  7036                                                                             324                                                                              7236                                                          SD: 16 0  2114                                                                             63 1467                                                          CV: 8.0                                                                              0   30                                                                              19.5                                                                             20.2                                                          Tests:                                                                            12 12  12                                                                              12 12                                            __________________________________________________________________________

Case #3:

Shown in Table E are examples of estimated plasma methadone levels forfour patients demonstrating how to detect misuse of methadone.

                  TABLE E                                                         ______________________________________                                        Utilization of Plasma Methadone Levels                                        To Uncover Misuse of Methadone                                                Estimated Plasma Methadone Concentration (ng/ml), p                           Sample Patient A*                                                                              Patient B  Patient C***                                                                           Patient D                                ______________________________________                                        1      480       346        89       1247****                                 2      465       234        44       1173****                                 3      485       281        50       1061****                                 4      525       233        334      1343****                                 5      454       376        84       435                                      6      410       208        310      575                                      7      531       290        778      427                                      8      483        172**     800      514                                      9      403        0**       33       474                                      ______________________________________                                         *Patient A ingests 90 mg/day of methadone q24 hr. as instructed. He           ingests a does in the clinic on Mon., Wed. and Fri., mean 24hr. trough        level is 470 ng/ml with a CV = 9.4%.                                          **Patient B receives 80 mg/day of methadone. She only gets a take home        dose for Sunday. Expected mean value (samples 1-6) is 281 +/- 62 ng/ml.       Sample 8 was taken 48 hr. after her last dose providing an estimate of        plasma methadone halflife of about 65 hrs. Sample 9 is an example of          substitution on a nonpatient urine sample.                                    ***Patient C ingests 50 mg/day in clinic on Mon., Wed. and Fri. Her           expected plasma concentration should be about 170 ng/ml. She is likely        diverting Tues, Thur. and Sun. take home doses and spiking urines with        exogenous methadone on other days. Solution was to withdraw take home         doses.                                                                        ****Patient D currently ingests 100 mg/day of methadone (samples 5-9).        Previously, he was ingesting over 200 mg/day of methadone via                 supplementing with illicit methadone (samples 1-4). Solution was to slowl     taper him back to 100 mg/day on a daily basis of clinic visits.          

Cases #4 and #5:

Shown in Tables F and G are data demonstrating how the statisticalprogram is utilized by the computer to `flag` a urine methadone value asbeing outside the acceptable range for the patient. With this data it ispossible for a healthcare provider to speak with a patient about thisabnormality before it becomes a continuing problem. Typically, laberrors are ruled out prior to discussion with the patient. Assuming nolaboratory explanation is forthcoming, the healthcare provider canconsider substitution of urine by the patient (often noted by variationin measured urinary parameters, including normalized creatine);ingestion of methadone on a non-24 hour basis; ingestion of additionaland unapproved methadone; selling of take-home methadone doses; taking amedication interfering with the metabolism of methadone and so forth.Having an objective and quantitative methadone history to present to thepatient overcomes the natural tendency for many patients to beuntruthful.

                                      TABLE F                                     __________________________________________________________________________    Date  Dose                                                                             Temp                                                                              pH SG  CR u   p  nu.sub.p                                                                          Pred                                        __________________________________________________________________________    09-10-93F                                                                           140                                                                              95.0                                                                              7.11                                                                             1.013                                                                             307                                                                              3631                                                                              352                                                                              17072                                                                             High                                        09-08-93W                                                                           140                                                                              95.0                                                                              5.19                                                                             1.025                                                                             306                                                                              12847                                                                             204                                                                              4686                                            09-02-93h                                                                           140                                                                              95.0                                                                              5.49                                                                             1.023                                                                             317                                                                              6345                                                                              154                                                                              3555                                            08-30-93M                                                                           140                                                                              95.0                                                                              4.68                                                                             1.023                                                                             316                                                                              12629                                                                             144                                                                              3269                                            08-26-93h                                                                           140                                                                              95.0                                                                              4.91                                                                             1.020                                                                             224                                                                              10227                                                                             186                                                                              4251                                            08-23-93M                                                                           120                                                                              94.0                                                                              4.91                                                                             1.025                                                                             239                                                                              14105                                                                             172                                                                              4466                                            08-20-93F                                                                           120                                                                              94.0                                                                              5.78                                                                             1.028                                                                             299                                                                              8194                                                                              172                                                                              4511                                            08-17-93T                                                                           120                                                                              94.0                                                                              5.31                                                                             1.026                                                                             311                                                                              8814                                                                              145                                                                              3768                                            08-13-93F                                                                           120                                                                              94.0                                                                              6.18                                                                             1.013                                                                             357                                                                              3101                                                                              314                                                                              8401                                            08-10-93T                                                                           120                                                                              95.0                                                                              5.81                                                                             1.021                                                                             296                                                                              4634                                                                              173                                                                              4550                                            08-06-93F                                                                           120                                                                              95.0                                                                              6.69                                                                             1.019                                                                             243                                                                              2923                                                                              252                                                                              6696                                            08-03-93T                                                                           120                                                                              95.0                                                                              5.53                                                                             1.024                                                                             185                                                                              8645                                                                              201                                                                              5264                                                            Mean:                                                                             283                                                                              8008                                                                              206                                                                              5130                                                            SD: 49 3945                                                                              67 1710                                                            CV: 17.3                                                                             49.2                                                                              32.4                                                                             33.3                                                            Tests:                                                                            12 12  12 11                                              __________________________________________________________________________

                                      TABLE G                                     __________________________________________________________________________    Date  Dose                                                                             Temp                                                                              pH  SG  CR  u   p  nu.sub.p                                                                          Pred                                      __________________________________________________________________________    08-06-93F                                                                           130                                                                              96.0                                                                              4.88                                                                              1.025                                                                              49L                                                                              4305                                                                              97 1858                                                                              LOW                                       08-02-93M                                                                           130                                                                              96.0                                                                              4.81                                                                              1.024                                                                             215 13601                                                                             163                                                                              5922                                          07-29-93h                                                                           130                                                                              96.0                                                                              5.05                                                                              1.019                                                                             211 11105                                                                             249                                                                              9089                                          07-26-93M                                                                           130                                                                              95.0                                                                              LOW 1.014                                                                             214 8822                                                                              163                                                                              5865                                          07-22-93h                                                                           130                                                                              96.0                                                                              4.52                                                                              1.028                                                                              42L                                                                              4431                                                                              98 1042                                                                              LOW                                       07-19-93M                                                                           130                                                                              95.0                                                                              4.66                                                                              1.021                                                                             258 25400                                                                             333                                                                              12050                                         07-15-93h                                                                           130                                                                              96.0                                                                              5.96                                                                              1.003                                                                             LOW 5585                                                                              381                                                                              97615                                                                             HIGH                                      07-12-93m                                                                           130                                                                              96.0                                                                              4.76                                                                              1.021                                                                             228 14361                                                                             208                                                                              7550                                          07-09-93F                                                                           130                                                                              94.0                                                                              4.76                                                                              1.015                                                                             230 10940                                                                             266                                                                              9563                                          07-06-93T                                                                           130                                                                              96.0                                                                              5.20                                                                              1.024                                                                             249 17816                                                                             309                                                                              11313                                         07-01-93h                                                                           130                                                                              96.0                                                                              5.10                                                                              1.012                                                                             224 6963                                                                              319                                                                              11630                                         06-28-93M                                                                           130                                                                              97.0                                                                              LOW 1.011                                                                             241 7478                                                                              190                                                                              6841                                          06-24-93h                                                                           130                                                                              N/T LOW 1.009                                                                             232 6889                                                                              224                                                                              8088                                                           Mean:                                                                             214 10585                                                                             231                                                                              8396                                                           SD:  41 6037                                                                              89 3288                                                           CV:  19.1                                                                             57  38.5                                                                             39.1                                                           Tests:                                                                             12 13  13 13                                            __________________________________________________________________________

Case #6:

Methadone concentration data were simultaneously measured using GC/MSand FPIA for urine obtained from five patients and plotted in FIG. 8 forcomparison. Linear regression analysis shows that GCMS=0.97*FPIA=48,R=0.999: both methods are essentially equivalent. Similarly, methodsother than GC/MS or FPIA could also be used, such as gas chromatography,high pressure liquid chromatography, chemical methods and so on, tosequentially follow raw urine methadone concentration patient data forutilization in this invention.

MEDICATION MAINTENANCE PROGRAMS

A patient is initially prescribed a medication and dose based on severalfactors. These ordinarily include the severity and duration of illness,amounts and types of medications previously used, current or previousphysiological and/or physical dependence upon other prescription orillicit drugs, previous medical history, patient sex, pregnancy status,patient weight and ingestion of other therapeutic medications. Normallymedication dose is adjusted upwardly until a patient no longer complainsof residual signs and symptoms of his or her psychiatric and/or medicalillness, is no longer experiencing withdrawal signs and symptoms if on amedication-replacement taper to abstinence program, or loses his or herdesire to use illicit medications if a substance abuse problem exists.Medication dose is increased per published and accepted standard medicalprotocols for each family of psychiatric and medical drug, usually "x"mg every few days.

To determine compliance with the prescribed medication dose, randomurine samples are obtained from the patient and analyzed in accordancewith the invention as described in FIG. 9. If tested and determined tobe unadulterated, a raw urine parent drug and/or its metabolitesconcentration is measured preferably using FPIA. Metabolites are thosesubstances which result from the body's metabolism of the parent drug.The metabolites are detectable and part of the value obtained whenmeasuring the raw urine medication concentration. The raw urinemedication concentration (u) is next converted to a normalized urinemedication concentration (nu) as discussed below. Over time, anormalized urine medication concentration-daily medication doserelationship is derived for each individual patient, which can becompared to the relationship expected for that particular patient.Alternatively, by adjusting the normalized urine medicationconcentration relative to the urinary pharmacokinetic parameters foreach medication, a urinary-parameter normalized urine medicationconcentration (nu_(p)) may be calculated and compared to that expectedfor an average patient to determine compliance with the patient'sprescribe medication dose.

Again, if the relationships between the present nu and the expected nuare not similar, either the patient's metabolism rate is causing anover- or under-effectiveness of the prescribed dose or the patient isnot complying with his or her prescribed dose. If related to thepatient's individual metabolism rate, a physician can now optimize thepatient's medication dose to achieve an efficacious and safe plasmamedication concentration. Once the optimum medication dose isestablished for the patient, a physician can monitor the patient forcompliance with his or her prescribed dose by comparing either the nu orthe nu_(p) with their expected values for the particular medicationdose; hence, uncovering covert medication diversion or supplementing.

The steps of testing for adultration of the urine sample anddetermination of the raw urine medication concentration are alsoutilized in determining compliance with a medication maintanence programand follow the same procedures as discussed above in methadonemaintanence programs.

Determination of Normalized Urine Medication Concentration

The normalized urine medication concentration, nu, is statisticallyconstant for each patient relative to the medication dose regardless ofan individual's medication metabolism (if the immunoreactivity for theFPIA antibody is nonselective between parent and drug metabolites) anddaily changes in urine parameters. In determining how to calculate nu,the linear relationship developed above between the urine volumeproduction rate factor (UVPRF) and the reverse urine creatinineexcretion factor (RUCEF) was utilized. This relationship, as shown inFIG. 4, is represented as follows:

    RUCEF=0.942(SE 0.013)·UVPRF+0.121(SE 0.043)       (13)

    u'/u=0.942·v/v'+0.121                             (14)

Therefore, contrary to the traditional teachings of those skilled in theart, urine drug and metabolite concentrations, u, are inversely relatedto the volume, v, of urine produced by the kidneys.

Following the same logic in determining plasma methadone concentrationequation, the standard dimensionally correct renal clearance equation isutilized, which is

    cl=(u·v)/p                                        (15)

Assuming that at steady-state plasma medication concentration and renalclearance are constant, the product (u·v) must also be constant at anyparticular time point. It follows that an empirical mathematicalrelationship exists between u and v such that given an arbitrary urinevolume production rate v' and an equivalent u' at a reference point(specific gravity 1.030):

    {u·v}.sub.sg actual ={u'·v'}.sub.sg 1.030(16)

or upon rearrangement for u' gives,

    u'=u·(v/v')                                       (17)

where the products given in Equations (16) and (17) are those measuredfor a spot urine collected with an actual specific gravity (u,v) and acorrected specific gravity typical of a morning void of 1.030 (u', v').Utilizing the linear relationship that exists between urine volumeproduction rate factor (UVPRF) and the specific gravity factor (SGF) inEquation (10) and combining it with Equation (17), a normalized urinemedication concentrations can be calculated as follows:

    nu=u'=u·(v/v')=u·UVPRF=u·(k.sub.1 ·SGF-k.sub.2)                                    (18)

wherein k₁ is a constant equal to 2.43 and k₂ is a constant equal to1.43.

Determination Of Urinary-Parameter Normalized Urine Concentration

The parameters of a patient's urine vary from one day to the nextdependant upon the type and quantities of foods and beverages ingested.Additionally, individuals metabolize these substances, as well asmedication, at different rates. By adjusting the normalized urinemedication concentration to account for these variations, theurinary-parameter normalized urine medication concentration (nu_(p)) iscalculated. Use of the nu_(p) is preferable in the clinical settingbecause nu_(p) is an alteration based on pharmacokinetic parametersimportant for a particular drug or family of drugs, thus providing avalue that may be compared to that expected of the average patient.

Some important pharmacokinetic parameters include: patient body weight,whether a drug is a weak acid or weak base, how a drug is absorbed intotissues and blood, how the drug is administered (ie., orally,intravenously), whether a drug is a controlled release formulation, howa drug distributes in the body (patient volume of distribution, proteinbinding, tissue binding, lipidicity, redistribution), whetherbiotransformation occurs (cross-reactive metabolites, chemicalhalf-life, tissue halflife), how the drug is excreted (renal clearance,hepatic clearance, tissue clearance, fecal clearance, dosing rate andamount, final steady-state concentrations of peak and trough levels ofdrug, zero order, first order or mixed order biotransformationreaction). These parameters may be measured by utilizing readilyavailable values such as patient body weight, prescribed medicationdose, urine pH, and urine volume production rate. For example, pH is animportant variable if one is monitoring weak bases such as methadone,but is of only minor importance when monitoring weak acids such as theglucuronide derivatives of benzodiazepines and opioids. Thepharmacokinetic parameters for each drug are available in medicalreferences such as Goodman & Gillman, The Pharmacological Basis ofTherapeutics, 8th Edition, Pergamon Press, 1990.

The relationships for any medication family between nu and themedication pharmacokinetic parameters are empirically developed usingregression analysis. For example, in the case of diazepam andalprazolam, urine pH is not important. However, the following equationlinearly adjusts each patient value to a standard weight of 70 kg (154lb) for useful results:

    nu.sub.p =(patient body weight/k.sub.3)·u·UVPRF(19)

wherein k₃ is a constant equal to 70. This value, once accuratelyestablished for a patient within a statistical margin of error, is usedto evaluate medication diversion or supplementation in the patient bycomparing subsequent calculations of this value with that an expectedvalue of the average patient. If the subsequent calculation is similarto the expected value, the patient is complying with his prescribeddose.

Statistical methods similar to those proposed for methadone can be usedto establish confidence limits.

Determining Daily Medication Dose Ingested

Once the urinary-parameter normalized urine medication concentration iscalculated from Equation (19), it and the patient's daily medicationdose are compared to that expected from a standard population. FIGS. 10and 11 show how urinary-parameter normalized urine medicationconcentration varies with dose for patients prescribed and properlyingesting diazepam and alprazolam. Using these graphs, a clinician canestimate how a change of dose will effect the patient's urine medicationconcentration. If a patient's urinary-parameter normalized urinemedication concentration is less than that expected from FIGS. 10 or 11,such a result may indicate that the patient is diverting the medicationto others or simply not using it. Higher concentrations per dose suggestthe opposite of the above.

A further appreciation for consistency of medication ingestion bypatients is shown in FIG. 12. The mean alprazolam normalizedconcentrations and standard deviations for several patients are plotted.As is apparent, all patients except one had SD of about ±15% of themean. The lone patient with a much higher variation was found to beingesting on average 4 mg alprazolam per day, ranging from 2 to 8 mg perday.

In general, it has been determined that most patients ingesting proper,prescribed dosages of medications produce a point-of-time, spot nu_(p)value that is often within ±20% of their individual mean value for anyparticular medication and dose. Although, actual acceptance values mustbe determined for each medication and assay method.

Two methods of interpreting urine medication results for compliancemonitoring have now been developed. The first and most primitive methodis to simply establish, using data from controls and compliant patients,mean drug levels and the expected ranges (minimums and maximums) for thenu_(p) of each particular medication at each particular daily, totaldose amount. For example, it has been determined that the followingequations for estimating the expected mean medication concentrations asa function of total, daily medication dose are useful for monitoring thebenzodiazepine parent drugs and metabolites using FPIA (temazepam,clonidine, flurazepam and oxazepam are similar to diazepam):

    Alprazolam: nu.sub.p =910(SE 31.4)*Dose, SEE 210           (20)

    Diazepam: nu.sub.p =267(SE 16.9)*Dose, SEE 806             (21)

Acceptable maximum and minimum ranges of the nu_(p) calculated byEquation (19) for any patient (after ruling out metabolic problems) aresimply given as ±20% of the expected mean value of nu_(p) at any dosefor a compliant patient as calculated by Equation (20) or (21).

A second and more sophisticated method for evaluating individualnormalized medication concentrations for a spot urine sample utilizesprobability theory and prediction intervals. To use this method, onecalculates mean and SD for each control and patient sample set and plotsthe SD for each subject versus size of each subject's sample set. Usingstandard prediction formulas and confidence limits on the population ofSD, one estimates from the actual data (each drug and drug family isunique) the true standard deviation for the population of all personsingesting the drug properly. Given this value for the true populationSD, other prediction equations can be derived of the form, acceptablevalue=patient mean ±x·SD, where x is a factor whose value is dependentupon sample size and desired confidence limit, e.g., 95, 97.5, 99, and99.999%. Once these values have been determined, the urinary-parameternormalized urine concentration calculated by Equation (19) can becompared to an expected range and noted as low, acceptable or high.

Given sufficient control and patient data and a method of analysis,preferably though not limited to quantitative immunoassay like FPIA,similar relationships for mean urinary-parameter normalized urinemedication concentrations as a functions of daily medication dose caneasily be derived both for other drugs in the benzodiazepine family andfor other distinctly different chemical families, making this methodbroadly useful. Therefore, this method is useful not only fordetermining the average amounts of medication taken each day, but howirregular the patient may be from one day to another.

Clinical Examples

Case #6:

J. W. is a 34 year old male presented for treatment of an anxietydisorder. He had been ingesting 1.5 mg alprazolam daily. After placingthe patient into an individualized, anxiety-reduction therapy program,his psychiatrist was able to gradually decrease his alprazolam toabstinence. The patient later attended college without evidence ofreturn to medication use. Shown in Table H is a partial representationof a standard computer printout for this compliant patient who wasslowly tapered from alprazolam using the nu_(p) method as an aid todownward dose adjustments. The last column in the figure marked BENZrepresents nu_(p) values for the patient which are quite constant oncespecific gravity and patient weight corrections are made to the rawurine medication concentration (u).

                  TABLE H                                                         ______________________________________                                        Date    Temp      pH     SG      CR   nu.sub.p, Ben                           ______________________________________                                        09-28-92M                                                                             98.0      5.40   1.024   253  280                                     09-22-92T                                                                             98.0      5.70   1.028   235  182                                     09-21-92M                                                                             96.0      5.10   1.025   279  228                                     09-17-92h                                                                             96.0      5.60   1.029   248  168                                     09-16-92W                                                                             98.0      5.30   1.028   199L 168                                     09-27-92h                                                                             98.0      5.40   1.025   234  184                                     09-24-f92M                                                                            98.0      5.50   1.029   289  162                                                              Mean:   257  196                                                              SD:      48  44                                                               CV:      9.6 21.9                                                             Tests:   12  7                                       08-14-92F                                                                             97.0      5.40   1.027   271  260                                     08-10-92M                                                                             97.0      5.40   1.029   260  388                                     08-06-92h                                                                             98.0      5.30   1.028   242  352                                     08-05-92W                                                                             98.0      5.80   1.029   234  306                                     07-29-92W                                                                             97.0      5.40   1.028   202L 252                                     07-27-92M                                                                             96.0      5.30   1.024   271  420                                     07-24-92F                                                                             98.0      5.70   1.024   244  522                                     07-20-92M                                                                             98.0      7.20   1.022   315  662                                     07-17-92F                                                                             97.0      6.60   1.029   219  426                                     07-15-92W                                                                             97.0      5.90   1.021   271  634                                                              Mean:   254  422                                                              SD:      28  144                                                              CV:      11.1                                                                              34.1                                                             Tests:   12  10                                      06-01-92M                                                                             97.0      5.80   1.030   286  718                                     05-27-92W                                                                             97.0      5.40   1.013   267  1032                                    05-26-92T                                                                             94.0      5.60   1.030   283  720                                     05-21-92h                                                                             98.0      6.00   1.021   286  830                                     05-19-92T                                                                             96.0      5.70   1.023   278  948                                     05-13-92W                                                                             98.0      5.60   1.029   241  670                                     05-09-92s                                                                             96.0      6.40   1.023   269  784                                     05-05-92T                                                                             96.0      5.50   1.018   284  1098                                    05-04-92M                                                                             98.0      5.70   1.027   256  840                                     04-30-92h                                                                             95.0      5.80   HI      277  940                                     04-27-92M                                                                             96.0      5.40   1.011   288  1200                                    04-24-92F                                                                             96.0      5.50   HI      277  826                                                              Mean:   274  884                                                              SD:      14  164                                                              CV:      5.1 18.4                                                             Tests:   12  12                                      04-20-92M                                                                             98.0      5.40   1.022   335  1164                                    04-15-92W                                                                             96.0      5.70   1.024   268  1014                                    04-13-92M                                                                             96.0      5.90   1.019   271  1174                                    04-10-92F                                                                             98.0      5.70   1.021   377H 1246                                    04-06-92M                                                                             98.0      5.90   1.028   261  858                                     04-02-92h                                                                             96.0      5.70   1.025   271  1052                                    03-30-92M                                                                             94.0      5.60   1.021   303  1512                                    03-25-92W                                                                             98.0      5.20   1.021   271  1346                                    03-24-92T                                                                             98.0      6.00   1.023   243  1330                                    03-20-92F                                                                             96.0      5.80   1.024   272  1278                                    03-16-92M                                                                             94.0      5.30   1.022   286  1464                                    03-13-92F                                                                             96.0      5.70   1.019   277  1710                                                             Mean:   285  1262                                                             SD:      32  234                                                              CV:      11.2                                                                              18.5                                                             Tests:   12  12                                      ______________________________________                                    

Case #7:

R. C. is a 38 year old long-term opiate addict who was prescribedalprazolam by an outside psychiatrist. This patient's drug use wasmonitored to insure that he was compliant with his prescription. Datafor this patient is shown in FIG. 12 and Table I. Table I is the urinedata sheet demonstrating large variation in the BENZ levels consistentwith irregular ingestion of alprazolam. FIG. 12 shows the elevated SDmeasured for this non-compliant patient as compared to others.

                  TABLE I                                                         ______________________________________                                        Date     Dose        pH    SG        Ben                                      ______________________________________                                        04-05-90  0          5.0   1.016     2896**                                   04-13-90 80          5.5   1.018     6128**                                   04-16-90 80          8.0   1.005     6252**                                   04-23-90 80          5.5   1.010     3358**                                   04-30-90 80          5.5   1.000     4110**                                   05-18-90 90          5.5   1.008     3322**                                   06-01-90 90          5.5   1.013     1512**                                   06-04-90 90          5.1   1.015     1790**                                   06-11-90 90          5.0   1.001     2468**                                   06-18-90 90          5.6   1.006     1836**                                   06-29-90 90          5.0   1.005     2664**                                   07-13-90 90          6.1   1.016      684**                                   07-16-90 90          5.5   1.001       0                                      07-27-90 90          5.1   1.006     3120**                                   07-30-90 90          5.0   1.005     2932**                                   08-06-90 90          5.5   1.015     2928**                                   08-15-90 90          7.1   1.009     2648**                                   08-20-90 90          5.0   1.018     2502**                                   08-29-90 90          5.6   1.016     2860**                                   09-04-90 90          6.5   1.025     HI**                                     09-05-90 90          6.1   1.019     3468**                                   09-10-90 90          5.0   1.013     4194**                                   09-24-90 90          7.0   1.005     4962**                                   10-01-90 90          5.0   1.010     6552**                                   10-02-90 90          6.1   1.010     2816**                                   10-08-90 90          5.1   1.023     2510**                                   ______________________________________                                         ***Xanax level: mean 4268 ng/ml, CV = 49.8% (normalized to 70 kg)        

Case #8:

A. S. is a 42 year old female requiring treatment of severe, episodicpain associated with spasm of the levator ani muscle of the pelvicfloor. She was prescribed Tylenol #3 (30 mg of codeine) po q8h forrelief of severe pain, prescribed Norflex 100 mg po bid to help relievereferred spasms of the buttock area and entered into a Rolfing programto realign her axial skeleton and balance the pelvic musculature.Following the above treatment plan her problem resolved over a 6 monthperiod allowing discontinuation of all medications other than occasionalNorflex. Shown in FIG. 13 are mean nu_(p) values for codeine as afunction of daily, total dose. Although the numbers are different,results are qualitatively similar to those seen with the benzodiazepinesand methadone. Her mean codeine level while stabilized on 90 mg ofcodeine qd, as shown on FIG. 13, should be 19,102 ±3840 ng/ml. A summaryof her weekly urine test results are also shown in Table J.

                  TABLE J                                                         ______________________________________                                        Date    Dose   Temp    pH    SG    CR   Coc  Opi                              ______________________________________                                        09-10-93F                                                                             9-0    94.0    LOW   1.013 42L       20471                            09-03-93F                                                                             9-0    95.0    5.60  1.017 343       15492                            08-27-93F                                                                             9-0    94.0    5.62  1.014 292       18659                            08-18-93W                                                                             9-0    96.0    5.50  1.022 355  0    21775                            08-03-93T                                                                             9-0    92.0    4.72  1.010 372       13830                            07-30-93F                                                                             9-0    94.0    5.53  1.023 390       20457                            07-16-93F                                                                             9-0    N/T     5.83  1.015 347  0    25039                            06-28-93M                                                                             9-0    96.0    6.10  1.017 383       21894                            06-18-93F                                                                             9-0    95.0    5.90  1.019 368       14297                                                         Mean: 349       19102                                                         SD:    34       3840                                                          CV:    9.5      20.1                                                          Tests:                                                                               9        9                                ______________________________________                                    

Case #9:

W. K. is a 44 year old male requiring opioid medications for severearachnoiditis following surgery in the lumber spine. He was prescribedoxycodone without acetaminophen since he is status post removal of onekidney because of renal carcinoma. Shown in Table K are his oxycodonelevels (40 mg per day total dose) which are within acceptable limits of800-1600 ng/ml.

                  TABLE K                                                         ______________________________________                                        Date    Temp      pH     SG      CR    nu.sub.p, Opi                          ______________________________________                                        02-14-94H                                                                             98.0      5.25   1.010   446H  1530Rx                                 02-10-94h                                                                             96.0      5.11   1.024   302    791Rx                                 02-07-94M                                                                             94.0      5.20   1.015   359   1154Rx                                 02-03-94h                                                                             96.0      5.33   1.011   186L  1062Rx                                 01-31-94M                                                                             N/T       7.13   1.017   299    928Rx                                 01-27-94h                                                                             N/T       5.21   1.013   286    583Rx                                 01-24-94M                                                                             N/T       5.41   1.011   264   1305Rx                                 01-20-94h                                                                             N/T       5.59   1.011   363    937Rx                                 01-17-94M                                                                             94.0      5.76   1.010   447H  1252Rx                                 01-13-94h                                                                             95.0      5.51   1.009   309   1562Rx                                 01-10-94M                                                                             94.0      5.44   1.012   415   1605Rx                                 01-06-94h                                                                             94.0      6.12   1.004   223   1760Rx                                                          Mean:   324   1206                                                            SD:      79    362                                                            CV:      24.4  30.0                                                           Tests:   12    12                                    ______________________________________                                    

It is thus seen that methods are now provided that monitor patients whohave been placed on medication maintenance programs for compliancewithout the need to draw blood. The invention utilizes readilyobtainable urine medication concentrations from evaluation of patienturine samples by FPIA to determine normalized and urinary-parameterurine medication concentration, which can be respectively compared tohistorical patient data and general population data to confirmprescription compliance. Plasma medication concentrations may also bedetermined. The methods are clinically practical without high laboratorytesting cost, the invasiveness of withdrawing blood, and the addedexposure to medical professionals of patient blood having highprobability of hepatitis and HIV infection.

While this invention has been described in detail with particularreference to preferred methods thereof, it should be understood thatmany modifications, additions and deletions may be made thereto withoutdeparture from the spirit and scope of the invention, includingapplication to other drugs and medications, as set forth in thefollowing claims.

What is claimed is:
 1. A method of monitoring compliance of a patientthat has been placed on a medication maintenance program with aprescribed medication dosage, and with the method comprising the stepsof(a) obtaining a sample of the patient's urine, (b) measuring theconcentration of the medication or its metabolites in the urine and theurine specific gravity, (c) calculating a normalized urine medicationconcentration as a function of the measured medication concentration inthe urine and the urine specific gravity in accordance with the equation

    un=u·(k.sub.1 ·SGF-k.sub.2)

where nu is the normalized urine medication concentration, u is themeasured concentration of medication in the urine, SGF is the specificgravity factor of the urine sample, and k₁ and k₂ are constants, and (d)comparing the normalized urine medication concentration with an expectedmedication concentration value for the patient for the maintenanceprogram prescribed to determine any significant differences therebetweenas an indication of noncompliance.
 2. A method of monitoring complianceof a patient that has been placed on a methadone maintenance programwith a prescribed methadone dosage, and with the method comprising thesteps of(a) obtaining a sample of the patient's urine, (b) measuring theconcentration of methadone in the urine, the specific gravity of theurine and the pharmacokinetic parameters of the medication includingmethadone dose, patient body weight, and urine pH, (c) calculating aurinary-parameter normalized urine methadone concentration as a functionof the measured methadone concentration in the urine, the urine specificgravity, the methadone dose, patient body weight, and urine pH, inaccordance with the equation

    nu.sub.p =(k.sub.3 /DOSE).sup.k4 ·(k.sub.5 /pH).sup.-k6 ·WGT/k.sub.7 ·u·(k.sub.1 ·SGF-k.sub.2)

where nu_(p) is the urinary-parameter normalized urine methadoneconcentration, DOSE is the prescribed methadone dose, pH is the pH ofthe urine sample, WGT is the patient body weight, SGF is the specificgravity factor of the urine sample, u is the measured concentration ofmethadone in the urine sample, and k₁ -k₇ are constants, and (d)comparing the urinary-parameter normalized urine methadone concentrationwith an expected methadone concentration value for an average compliantpatient for the maintenance program prescribed to determine anysignificant differences therebetween as an indication of noncompliance.3. A method of monitoring compliance of a patient that has been placedon a methadone maintenance program which comprises the steps of(a)obtaining a sample of the patient's urine, (b) measuring theconcentration of methadone, the specific gravity and the pH value of theurine sample, (c) calculating the concentration of methadone of theplasma as a function of the measured concentration of methadone of theurine, urine specific gravity and urine pH in accordance with theequation

    p=k.sub.3 u·(k.sub.1 SGF-k.sub.2)/k.sub.4 ·pH.sup.k5

where p is the calculated plasma methadone concentration, u is themeasured urine methadone concentration, SGF is the specific gravityfactor of the patient's urine, pH is the measured pH value of the urine,and k₁, k₂, k₃, k₄, and k₅ are constants, and (d) comparing thecalculated concentration of methadone of the plasma with an expectedvalue for the maintenance program prescribed.